Question

Let $\overline{XY}$ be a tangent to a circle, and let $\overline{XBA}$ be a secant of the circle, as shown below. If $AX = 15$ and $XY = 9$, then what is $AB$?

Answer 1

The length of segment AB is calculated using the Power of a Point theorem by setting up the equation AX × AB = XY² and solving for AB, which results in AB being 6 units long.

Step-by-step explanation:

To find the length of AB, we can use the properties of secants and tangents in a circle. The Power of a Point theorem states that the product of the lengths of the two segments of a secant line from a point outside the circle to the points of intersection with the circle equals the square of the length of the tangent segment from that point to the point of tangency with the circle.

Using the given lengths, we can set up the equation: AX × AB = XY². Plugging in the values, we get 15 × AB = 9². To solve for AB, divide both sides by 15, which gives us AB = 9² / 15 = 6. Thus, AB = 6.

Answer 2

Its 9.6, the other guy got it wrong, he already got it but accidentally added a step. Its 9.6 :)

Step-by-step explanation:

trust me :).